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The Hausdorff Moment Problem under Finite Additivity

Author

Listed:
  • Enrique Miranda

    (Rey Juan Carlos University)

  • Gert Cooman

    (Ghent University, Systems Research Group)

  • Erik Quaeghebeur

    (Ghent University, Systems Research Group)

Abstract

We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.

Suggested Citation

  • Enrique Miranda & Gert Cooman & Erik Quaeghebeur, 2007. "The Hausdorff Moment Problem under Finite Additivity," Journal of Theoretical Probability, Springer, vol. 20(3), pages 663-693, September.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:3:d:10.1007_s10959-007-0055-4
    DOI: 10.1007/s10959-007-0055-4
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